change a position's mate score from 19 to 21

[robertnurnberg]

This PR proposes to raise the bm value for the position 8/2p5/7p/2pR3r/8/6R1/2P4r/4K2k w - - from 19 to 21, see also #52. The new entry in matetrack.epd reads

8/2p5/7p/2pR3r/8/6R1/2P4r/4K2k w - - bm #21; c0 "was bm #19";

The position is well explored on cdb, with also the second best of white's moves along the mating line analysed within cdb to the checkmate leaf node (if it also leads to mate). It seems the puzzle composer simply forgot about the move 16..Rf5+, with the next best alternative moves leading to mate in 19.

I have also done a local backward analysis, using the command python provepvs.py --epdFile mate21.epd --cdbFile mate21pv.epd --engine stockfish --threads 1 --hash 8192 --depth 200 --time 7200 --depthMin 200 --depthMax 200 --timeFill 3600 >& log.txt &. The output of which is as below:

Output

Found 1 PVs we can use to try to prove/find mate PVs ...
1/1 "8/2p5/7p/2pR3r/8/6R1/2P4r/4K2k w - -" with bm #21...
Analysing "8/8/8/3R3p/2p5/2p2K1k/2P5/8 w - -" (after move h4h3) to Limit(time=3600.0, depth=200).
ply  40, score #+1 (d200, nodes 3800) PV: d5h5
Analysing "8/8/8/3R3p/2p4k/2p2K2/2P5/8 b - -" (after move f5d5) to Limit(time=3600.0, depth=200).
ply  39, score #-1 (d200, nodes 400) PV: h4h3 d5h5
Analysing "8/8/8/5R1p/2p4k/2p2K2/2P5/8 w - -" (after move h6h5) to Limit(time=3600.0, depth=200).
ply  38, score #+2 (d200, nodes 6809) PV: f5d5 h4h3 d5h5
Analysing "8/8/7p/5R2/2p4k/2p2K2/2P5/8 b - -" (after move f2f3) to Limit(time=3600.0, depth=200).
ply  37, score #-2 (d200, nodes 4123) PV: h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/5R2/2p4k/2p5/2P2K2/8 w - -" (after move h3h4) to Limit(time=3600.0, depth=200).
ply  36, score #+3 (d200, nodes 101327) PV: f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/5R2/2p4R/2p4k/2P2K2/8 b - -" (after move g4h4) to Limit(time=3600.0, depth=200).
ply  35, score #-3 (d200, nodes 7405) PV: h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/5R2/2p3Rr/2p4k/2P2K2/8 w - -" (after move h2h3) to Limit(time=3600.0, depth=200).
ply  34, score #+4 (d200, nodes 1569979) PV: g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/5R2/2p3Rr/2p5/2P2K1k/8 b - -" (after move e5f5) to Limit(time=3600.0, depth=200).
ply  33, score #-4 (d200, nodes 27578) PV: h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4Rr2/2p3Rr/2p5/2P2K1k/8 w - -" (after move h5f5) to Limit(time=3600.0, depth=200).
ply  32, score #+5 (d200, nodes 106895) PV: e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4R2r/2p3Rr/2p5/2P2K1k/8 b - -" (after move f1f2) to Limit(time=3600.0, depth=200).
ply  31, score #-5 (d200, nodes 24790) PV: h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4R2r/2p3Rr/2p5/2P4k/5K2 w - -" (after move h1h2) to Limit(time=3600.0, depth=200).
ply  30, score #+6 (d200, nodes 10970451) PV: f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4R2r/2p3Rr/2p5/2P5/5K1k b - -" (after move g2g4) to Limit(time=3600.0, depth=200).
ply  29, score #-6 (d200, nodes 75863) PV: h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4R2r/2p4r/2p5/2P3R1/5K1k w - -" (after move h2h1) to Limit(time=3600.0, depth=200).
ply  28, score #+7 (d200, nodes 46007279) PV: g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4R2r/2p4r/2p5/2P3Rk/5K2 b - -" (after move g1g2) to Limit(time=3600.0, depth=200).
ply  27, score #-7 (d200, nodes 1906834) PV: h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4R2r/2p4r/2p5/2P4k/5KR1 w - -" (after move h1h2) to Limit(time=3600.0, depth=200).
ply  26, score #+8 (d200, nodes 729900227) PV: g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4R2r/2p4r/2p5/2P5/5KRk b - -" (after move g4g1) to Limit(time=3600.0, depth=200).
ply  25, score #-8 (d200, nodes 351760) PV: h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/4R2r/2p3Rr/2p5/2P5/5K1k w - -" (after move c5c4) to Limit(time=3600.0, depth=200).
ply  24, score #+9 (d149, nodes 6347608404) PV: g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/2p1R2r/6Rr/2p5/2P5/5K1k b - -" (after move g2g4) to Limit(time=3600.0, depth=200).
ply  23, score #-9 (d155, nodes 4312478505) PV: c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/2p1R2r/7r/2p5/2P3R1/5K1k w - -" (after move h2h1) to Limit(time=3600.0, depth=200).
ply  22, score #+10 (d158, nodes 6498629555) PV: g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/2p1R2r/7r/2p5/2P3Rk/5K2 b - -" (after move g1g2) to Limit(time=3600.0, depth=200).
ply  21, score #-10 (d161, nodes 2466981029) PV: h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/2p1R2r/7r/2p5/2P4k/5KR1 w - -" (after move h1h2) to Limit(time=3600.0, depth=200).
ply  20, score #+11 (d133, nodes 5071639978) PV: g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/2p1R2r/7r/2p5/2P5/5KRk b - -" (after move g4g1) to Limit(time=3600.0, depth=200).
ply  19, score #-11 (d140, nodes 3647393275) PV: h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/7p/2p1R2r/6Rr/2p5/2P5/5K1k w - -" (after move c6c5) to Limit(time=3600.0, depth=200).
ply  18, score #+12 (d119, nodes 5317324398) PV: g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/2p4p/4R2r/6Rr/2p5/2P5/5K1k b - -" (after move g2g4) to Limit(time=3600.0, depth=200).
ply  17, score #-12 (d127, nodes 1418564206) PV: c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/2p4p/4R2r/7r/2p5/2P3R1/5K1k w - -" (after move h2h1) to Limit(time=3600.0, depth=200).
ply  16, score #+13 (d101, nodes 4951127329) PV: g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/2p4p/4R2r/7r/2p5/2P3Rk/5K2 b - -" (after move g1g2) to Limit(time=3600.0, depth=200).
ply  15, score #-13 (d109, nodes 3574621936) PV: h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/2p4p/4R2r/7r/2p5/2P4k/5KR1 w - -" (after move h1h2) to Limit(time=3600.0, depth=200).
ply  14, score #+14 (d77, nodes 4852314530) PV: g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/2p4p/4R2r/7r/2p5/2P5/5KRk b - -" (after move g4g1) to Limit(time=3600.0, depth=200).
ply  13, score #-14 (d84, nodes 3897252913) PV: h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/8/2p4p/4R2r/6Rr/2p5/2P5/5K1k w - -" (after move c7c6) to Limit(time=3600.0, depth=200).
ply  12, score #+15 (d72, nodes 4995093142) PV: g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/4R2r/6Rr/2p5/2P5/5K1k b - -" (after move g2g4) to Limit(time=3600.0, depth=200).
ply  11, score #-15 (d74, nodes 4233237361) PV: c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/4R2r/7r/2p5/2P3R1/5K1k w - -" (after move h2h1) to Limit(time=3600.0, depth=200).
ply  10, score #+16 (d70, nodes 5414457596) PV: g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/4R2r/7r/2p5/2P3Rk/5K2 b - -" (after move g1g2) to Limit(time=3600.0, depth=200).
ply   9, score #-16 (d73, nodes 323029247) PV: h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/4R2r/7r/2p5/2P4k/5KR1 w - -" (after move h1h2) to Limit(time=3600.0, depth=200).
ply   8, score #+17 (d64, nodes 4902182883) PV: g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/4R2r/7r/2p5/2P5/5KRk b - -" (after move g4g1) to Limit(time=3600.0, depth=200).
ply   7, score #-17 (d62, nodes 4862495) PV: h1h2 g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/4R2r/6Rr/2p5/2P5/5K1k w - -" (after move c4c3) to Limit(time=3600.0, depth=200).
ply   6, score #+18 (d55, nodes 5293898090) PV: g4g1 h1h2 g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/4R2r/2p3Rr/8/2P5/5K1k b - -" (after move d5e5) to Limit(time=3600.0, depth=200).
ply   5, score #-18 (d62, nodes 3599158800) PV: c4c3 g4g1 h1h2 g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/3R3r/2p3Rr/8/2P5/5K1k w - -" (after move c5c4) to Limit(time=3600.0, depth=200).
ply   4, score #+19 (d47, nodes 5564567144) PV: d5e5 c4c3 g4g1 h1h2 g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/2pR3r/6Rr/8/2P5/5K1k b - -" (after move g3g4) to Limit(time=3600.0, depth=200).
ply   3, score #-19 (d58, nodes 2374936812) PV: c5c4 d5e5 c4c3 g4g1 h1h2 g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/2pR3r/7r/6R1/2P5/5K1k w - -" (after move h2h4) to Limit(time=3600.0, depth=200).
ply   2, score #+20 (d58, nodes 5470314143) PV: g3g4 c5c4 d5e5 c4c3 g4g1 h1h2 g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/2pR3r/8/6R1/2P4r/5K1k b - -" (after move e1f1) to Limit(time=3600.0, depth=200).
ply   1, score #-20 (d58, nodes 127093874) PV: h2h4 g3g4 c5c4 d5e5 c4c3 g4g1 h1h2 g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Analysing "8/2p5/7p/2pR3r/8/6R1/2P4r/4K2k w - -" to Limit(time=7200.0, depth=200).
Final score #+21, mate 21 (d52, nodes 11572193617) PV: e1f1 h2h4 g3g4 c5c4 d5e5 c4c3 g4g1 h1h2 g1g2 h2h1 g2g4 c7c6 g4g1 h1h2 g1g2 h2h1 g2g4 c6c5 g4g1 h1h2 g1g2 h2h1 g2g4 c5c4 g4g1 h1h2 g1g2 h2h1 g2g4 h1h2 f1f2 h5f5 e5f5 h2h3 g4h4 h3h4 f2f3 h6h5 f5d5 h4h3 d5h5
Found mate #21!
PV has status ok and length 41 > 0.
Save PV to file.
All done. Saved 1 PVs to provenpvs.epd.

The output confirms the mate scores along the mating line, to in general very high depths. Combined with the relatively few pieces, the relatively low piece mobility and the rather short mate length, this is a strong indication that the best mate for this position is indeed a mate in 21.

PS: Note also the very deep analysis in #52 (comment).